Maybe you should start experimenting with the sound card of a PC, focusing in the software side. The sample rate and resolution of a sound card is much better than of the bitalino, so after acquisition you can "degrade" the signal in the software to simulate a bitalino acquired signal. Then you can verify what specs are really needed to achieve your objectives.
For example, compare the results of the signal analysis using different resolutions, 6 bits and 10 bits (the resolutions of bitalino board) and using higher resolutions too.
Do the same with the sample rate.
It is very important to consider the signal conditioning before the ADC. You want to use a Low Pass Filter to avoid aliasing, and amplify/attenuate the signal to make better use of the ADC input range.
If you are going to need that much channels (18 or more), maybe a dedicated DAQ board is better than the multiple sound cards approach.